High-Voltage Polyanion Positive Electrode Materials

High-voltage generation (over 4 V versus Li+/Li) of polyanion-positive electrode materials is usually achieved by Ni3+/Ni2+, Co3+/Co2+, or V4+/V3+ redox couples, all of which, however, encounter cost and toxicity issues. In this short review, our recent efforts to utilize alternative abundant and less toxic Fe3+/Fe2+ and Cr4+/Cr3+ redox couples are summarized. Most successful examples are alluaudite Na2Fe2(SO4)3 (3.8 V versus sodium and hence 4.1 V versus lithium) and β1-Na3Al2(PO4)2F3-type Na3Cr2(PO4)2F3 (4.7 V versus sodium and hence 5.0 V versus lithium), where maximizing ΔG by edge-sharing Fe3+-Fe3+ Coulombic repulsion and the use of the 3d2/3d3 configuration of Cr4+/Cr3+ are essential for each case. Possible exploration of new high-voltage cathode materials is also discussed.


Introduction
Polyanion-positive electrode material for lithium batteries was identified by Delmas, Goodenough, and their co-workers for the NASICON M 2 (XO 4 ) 3 framework in the 1980s [1][2][3]. Later on, Padhi, Nanjundaswamy, and Goodenough discovered a very promising positive electrode material, LiFePO 4 [4], which is now widely commercialized for stationary use or a power source for electric vehicles. A common advantage of polyanion-type electrodes is their long-term stability of operation due to the rigid structural framework. Additional advantages inherent to LiFePO 4 that have led to its commercial application are (i) lithium can be extracted at the first charge and functions as a charge carrier, moving back and forward upon charge/discharge, (ii) it can withstand self-decomposition to guarantee a high level of safety, and (iii) it has a suitable operating voltage of 3.4 V versus lithium, which is not so high that it decomposes electrolytes but not too low that energy density is sacrificed [5].
Toward higher voltages, Mn analogue LiMnPO 4 (4.1 V versus lithium) was investigated but its low electrochemical activity was not acceptable, and this negative feature is common for all Mn-based polyanion-positive electrode materials [4,[6][7][8]. Vanadium-based compounds such as LiVPO 4 F [9] operate well at a reasonable voltage range around 4.2 V, but they have been excluded as a commercial option due to the element's toxicity and the volume change during Li + de/intercalation [10,11]. For an even higher voltage, Co 3+ /Co 2+ and Ni 3+ /Ni 2+ redox couples show activity at >4.5 V [12][13][14], but their highly oxidizing nature induces several side reactions unless careful design is applied to both the electrolyte and electrode composite. For a sodium analogue, electrode operation at higher voltages is more important as the Na/Na + potential is ca. 0.3 V higher than the Li/Li + potential. Within the polyanionic materials, strategic design toward high-voltage operation is almost the same in the case of lithium, achieved by introducing V, Co, Ni as a redox center, as represented by Na 4 Co 3 (PO 4 ) 2 P 2 O 7 [15][16][17].
However, the use of V, Co, or Ni is a challenging option for battery engineers as they entail cost and toxicity issues. In particular, for a sodium battery system, a highvoltage system with more abundant and cheap elements would be ideal. In this short review article, after summarizing the influential factors dominating positive electrode  [18] and β 1 -Na 3 Al 2 (PO 4 ) 2 F 3 -type Na 3 Cr 2 (PO 4 ) 2 F 3 (4.7 V versus sodium and hence 5.0 V versus lithium) [19], will be demonstrated.

Inductive Effect in Polyanionic Compounds
The voltage trend of polyanion-based positive electrode materials roughly follows the formal charges of the central atoms in the polyanions, consisting of the idea of the inductive effect [20]. The presence of strong X-O covalency stabilizes the antibonding M 3+ /M 2+ state through an M-O-X inductive effect to generate an appropriately high voltage. A series of compounds including large polyanions (XO 4 ) y− (X = S, P, As, Mo, W, y = 2 or 3) were explored, and the use of (PO 4 ) 3− and (SO 4 ) 2− has been shown to stabilize the structure and lower the M 3+ /M 2+ redox energy to useful levels.

Thermodynamic Modification
In essence, the voltage is defined as the difference between the lithium chemical potential in the cathode and in the anode, leading to a simple thermodynamic definition, ignoring PV and TS terms: (P = pressure, V = volume, T = temperature, and S = entropy), E = (G Li + G charged − G discharged )/nF. where G Li , G charged , and G discharged , are the Gibbs free energies of lithium metal, charged cathode, and discharged cathode, respectively; n is the number of electrons in the redox reaction, and F is the Faraday constant. The overall thermodynamic scheme for voltage generation is summarized in Figure 1 based on the Born-Haber cycle [21].

Inductive Effect in Polyanionic Compounds
The voltage trend of polyanion-based positive electrode materials roughly follows the formal charges of the central atoms in the polyanions, consisting of the idea of the inductive effect [20]. The presence of strong X-O covalency stabilizes the antibonding M 3+ /M 2+ state through an M-O-X inductive effect to generate an appropriately high voltage. A series of compounds including large polyanions (XO4) y− (X = S, P, As, Mo, W, y = 2 or 3) were explored, and the use of (PO4) 3− and (SO4) 2− has been shown to stabilize the structure and lower the M 3+ /M 2+ redox energy to useful levels.

Thermodynamic Modification
In essence, the voltage is defined as the difference between the lithium chemical potential in the cathode and in the anode, leading to a simple thermodynamic definition, ignoring PV and TS terms: (P = pressure, V = volume, T = temperature, and S = entropy), E = (GLi + Gcharged − Gdischarged)/nF. where GLi, Gcharged, and Gdischarged, are the Gibbs free energies of lithium metal, charged cathode, and discharged cathode, respectively; n is the number of electrons in the redox reaction, and F is the Faraday constant. The overall thermodynamic scheme for voltage generation is summarized in Figure 1 based on the Born-Haber cycle [21]. The notations R and R* represent relaxed and unrelaxed frameworks, respectively. Bulk ionization energy, which is closely related to the inductive effect, is an approximation (electronic part) but is not identical to ΔG. Figure 2 shows a schematic derivation of the operation voltages and d-band positions of 3d transition metal phosphates in sodium ion batteries. [19] In general, a transition metal ion M n+ with a higher atomic number has a deeper valence level owing to a larger effective nuclear charge, resulting in a higher M (n+1)+ /M n+ redox potential. Naturally, phosphates with end representatives of the 3d series, such as Co 2+ and Ni 2+ , typically Na2CoPO4F and Na4M3(PO4)2P2O7 (M = Co 2+ and Ni 2+ ), have been reported as high-voltage (4.3 V, 4.4 V, 4.8 V, respectively) cathode materials [16,17,[22][23][24]. However, end representatives of the 3d series suffer from energy-level increments either by spin exchange penalty or crystal field splitting. On the other hand, the 3d 3 electron of Cr 3+ in the t2g orbital is free The notations R and R* represent relaxed and unrelaxed frameworks, respectively. Bulk ionization energy, which is closely related to the inductive effect, is an approximation (electronic part) but is not identical to ∆G. Figure 2 shows a schematic derivation of the operation voltages and d-band positions of 3d transition metal phosphates in sodium ion batteries. [19] In general, a transition metal ion M n+ with a higher atomic number has a deeper valence level owing to a larger effective nuclear charge, resulting in a higher M (n+1)+ /M n+ redox potential. Naturally, phosphates with end representatives of the 3d series, such as Co 2+ and Ni 2+ , typically Na 2 CoPO 4 F and Na 4 M 3 (PO 4 ) 2 P 2 O 7 (M = Co 2+ and Ni 2+ ), have been reported as high-voltage (4.3 V, 4.4 V, 4.8 V, respectively) cathode materials [16,17,[22][23][24]. However, end representatives of the 3d series suffer from energy-level increments either by spin exchange penalty or crystal field splitting. On the other hand, the 3d 3 electron of Cr 3+ in the t 2g orbital is free from both spin exchange and crystal field splitting, which can be compensated for the smaller nuclear charge. Indeed, Cr 4+ /Cr 3+ redox couples in phosphates generate >4.5 V vs. Na/Na + (as presented below) [19], comparable to Co-or Ni-based phosphates. from both spin exchange and crystal field splitting, which can be compensated for the smaller nuclear charge. Indeed, Cr 4+ /Cr 3+ redox couples in phosphates generate >4.5 V vs. Na/Na + (as presented below) [19], comparable to Co-or Ni-based phosphates.  [19]. 10Dq and ΔEex indicate an octahedral crystal field splitting energy for 3d orbitals and exchange splitting energy, respectively. Orange and blue shading corresponds to valences of 3 and 2, respectively. Note that there is also a contribution of the Madelung and other energies to the cell voltage that is superimposed on the electronic contribution of the transition metal ions (see Figure 1). Permission is granted by Chemistry of Materials.

Pyrophosphates
Of particular interest is the triplite phase of LiFeSO 4 F [25] and metal-doped Li 2 FeP 2 O 7 [26,27] possess edge-sharing FeO6 octahedra to minimize the Fe-Fe distance, as distinguished from other, lower-voltage Fe-based polyanion electrodes with corner-sharing octahedra. A shorter Fe 3+ -Fe 3+ distance in the charged state is effective for enlarging Gcharged, and hence the operating voltage E, while the influence of the discharged state Gdischarged with smaller charge Fe 2+ can be subordinated in energetics.
The cell voltage for these two materials can reach as high as 3.9 V (vs. Li), which is higher than the value of 3.8 V calculated from the standard redox potentials. The latter has been suggested to be the highest achievable voltage for a Li ion battery utilizing the Fe 3+ /Fe 2+ redox couple in solid. As shown in Figure 3, the potential tunability for the Fe 3+ /Fe 2+ redox couple at the unusually high-voltage region of 3.5-3.9 V vs. lithium is similar for any metal M doping in the Li2MxFe1-xP2O7 system [27]. The phenomena include two aspects: (1) two redox reactions at different potentials are stabilized with the doping of foreign metal M, (2) with more dopant, both of the redox reactions upshift to higher potential, and one even approaches 4 V. Substitution of M into Fe sites may suppress the migration of Fe from the FeO5 site upon charging, and the two original, distinct Fe sites become robust to stabilize the edge-sharing geometry of FeO5 and FeO6 polyhedrals with large Fe 3+ -Fe 3+ coulombic repulsion energy, leading to the two distinct redox reactions with inherently high potentials. The change in the relative energy of the intermediate compounds, which is induced by the unfavorable VLi ' -M 2+ (MFe × ) and/or LiLi × -Fe 3+ (FeFe•) interaction in the doping case, may be a reason for the further potential upshifting. The classic inductive effect cannot explain the redox potential upshifting phenomenon in this case.  [19]. 10Dq and ∆E ex indicate an octahedral crystal field splitting energy for 3d orbitals and exchange splitting energy, respectively. Orange and blue shading corresponds to valences of 3 and 2, respectively. Note that there is also a contribution of the Madelung and other energies to the cell voltage that is superimposed on the electronic contribution of the transition metal ions (see Figure 1). Permission is granted by Chemistry of Materials.

Pyrophosphates
Of particular interest is the triplite phase of LiFeSO4F [25] and metal-doped Li2FeP2O7 [26,27] possess edge-sharing FeO 6 octahedra to minimize the Fe-Fe distance, as distinguished from other, lower-voltage Fe-based polyanion electrodes with corner-sharing octahedra. A shorter Fe 3+ -Fe 3+ distance in the charged state is effective for enlarging G charged , and hence the operating voltage E, while the influence of the discharged state G discharged with smaller charge Fe 2+ can be subordinated in energetics.
The cell voltage for these two materials can reach as high as 3.9 V (vs. Li), which is higher than the value of 3.8 V calculated from the standard redox potentials. The latter has been suggested to be the highest achievable voltage for a Li ion battery utilizing the Fe 3+ /Fe 2+ redox couple in solid. As shown in Figure 3, the potential tunability for the Fe 3+ /Fe 2+ redox couple at the unusually high-voltage region of 3.5-3.9 V vs. lithium is similar for any metal M doping in the Li 2 M x Fe 1-x P 2 O 7 system [27]. The phenomena include two aspects: (1) two redox reactions at different potentials are stabilized with the doping of foreign metal M, (2) with more dopant, both of the redox reactions upshift to higher potential, and one even approaches 4 V. Substitution of M into Fe sites may suppress the migration of Fe from the FeO 5 site upon charging, and the two original, distinct Fe sites become robust to stabilize the edge-sharing geometry of FeO 5 and FeO 6 polyhedrals with large Fe 3+ -Fe 3+ coulombic repulsion energy, leading to the two distinct redox reactions with inherently high potentials. The change in the relative energy of the intermediate compounds, which is induced by the unfavorable V Li ' -M 2+ (M Fe × ) and/or Li Li × -Fe 3+ (Fe Fe •) interaction in the doping case, may be a reason for the further potential upshifting. The classic inductive effect cannot explain the redox potential upshifting phenomenon in this case. Molecules 2021, 26, x FOR PEER REVIEW 4 of 6 Figure 3. Schematic description of free energy difference between starting and delithiation materials. The right-hand portion is the pristine Li2FeP2O7 system. The spontaneous structural rearrangement (Fe's migration) destroys the edge-sharing configuration and decreases the free energy of the delithiated state, which results in an energy difference of △E1. The left-hand portion is the doping system Li2MxFe1-xP2O7. After full delithiation, the Li concentration is higher than that in the Li2FeP2O7 case, because all of the M ions remain inert. The remaining Li can block the Fe migration and can stabilize the Fe's original local structure and the whole crystal structure, which means that the energy difference △E2 should be higher than △E1.

Alluaudites
Compaction of the MO6 dimer can be more pronounced in an alluaudite framework, where two edge-shared MO6 octahedra are bridged by a small XO4 tetrahedron and the M-M distance becomes much shorter (Figure 4). During the search along the Na2SO4-FeSO4 tie line, we discovered the first sulfate compound with an alluaudite-type framework [18]. Deviating sharply from most of the AxM2(XO4) 3  The Na2Fe2(SO4)3 offers an average potential of 3.8 V (vs. Na/Na + ), with smooth, sloping charge-discharge profiles over a narrow voltage range of 3.3-4.3 V, which is the highest Fe 3+ /Fe 2+ redox potential obtained in any material environment ( Figure 5). [18] The abnormally high voltage can be explained by the thermodynamic definition of voltage explained in Section 2.2; the edge-sharing geometry of the Fe octahedra in Na2Fe2(SO4)3 will raise Gcharged due to the strong Fe 3+ -Fe 3+ repulsion, leading to high E. Additionally, it offers excellent rate kinetics and cycling stability without requiring any additional cathode optimization. It forms an open framework host for the efficient (de)intercalation of Na ions with very low activation energy.

Edge-shared FeO 6
Corner-shared SO 4 Figure 3. Schematic description of free energy difference between starting and delithiation materials. The right-hand portion is the pristine Li 2 FeP 2 O 7 system. The spontaneous structural rearrangement (Fe's migration) destroys the edge-sharing configuration and decreases the free energy of the delithiated state, which results in an energy difference of E 1 . The left-hand portion is the doping system Li 2 M x Fe 1-x P 2 O 7 . After full delithiation, the Li concentration is higher than that in the Li 2 FeP 2 O 7 case, because all of the M ions remain inert. The remaining Li can block the Fe migration and can stabilize the Fe's original local structure and the whole crystal structure, which means that the energy difference E 2 should be higher than E 1 .

Alluaudites
Compaction of the MO 6 dimer can be more pronounced in an alluaudite framework, where two edge-shared MO 6 octahedra are bridged by a small XO 4 tetrahedron and the M-M distance becomes much shorter (Figure 4). During the search along the Na 2 SO 4 -FeSO 4 tie line, we discovered the first sulfate compound with an alluaudite-type framework [18]. Deviating sharply from most of the A x M 2 (XO 4 ) 3 -type compounds adopting the NASICONrelated structures, Na 2 Fe 2 (SO 4 ) 3 does not contain the lantern units [M 2 (XO 4 ) 3 ]. It would be convenient to denote AA'BM 2 (XO 4 ) 3 as general alluaudite-type compounds, where A = partially occupied Na(2), A' = partially occupied Na(3), B = Na(1), M = Fe 2+ , and X = S in the present case.
Molecules 2021, 26, x FOR PEER REVIEW Figure 3. Schematic description of free energy difference between starting and delithiation m als. The right-hand portion is the pristine Li2FeP2O7 system. The spontaneous structural rearr ment (Fe's migration) destroys the edge-sharing configuration and decreases the free energy delithiated state, which results in an energy difference of △E1. The left-hand portion is the d system Li2MxFe1-xP2O7. After full delithiation, the Li concentration is higher than that in the Li2F case, because all of the M ions remain inert. The remaining Li can block the Fe migration an stabilize the Fe's original local structure and the whole crystal structure, which means that th ergy difference △E2 should be higher than △E1.

Alluaudites
Compaction of the MO6 dimer can be more pronounced in an alluaudite framew where two edge-shared MO6 octahedra are bridged by a small XO4 tetrahedron an M-M distance becomes much shorter (Figure 4). During the search along the Na FeSO4 tie line, we discovered the first sulfate compound with an alluaudite-type fr work [18].  The Na2Fe2(SO4)3 offers an average potential of 3.8 V (vs. Na/Na + ), with smooth, ing charge-discharge profiles over a narrow voltage range of 3.3-4.3 V, which is the est Fe 3+ /Fe 2+ redox potential obtained in any material environment ( Figure 5). [18] Th normally high voltage can be explained by the thermodynamic definition of voltag plained in Section 2.2; the edge-sharing geometry of the Fe octahedra in Na2Fe2(SO4) raise Gcharged due to the strong Fe 3+ -Fe 3+ repulsion, leading to high E. Additionally, it o excellent rate kinetics and cycling stability without requiring any additional cathod timization. It forms an open framework host for the efficient (de)intercalation of Na with very low activation energy.

Edge-shared FeO 6
Corner-shared SO 4 The Na 2 Fe 2 (SO 4 ) 3 offers an average potential of 3.8 V (vs. Na/Na + ), with smooth, sloping charge-discharge profiles over a narrow voltage range of 3.3-4.3 V, which is the highest Fe 3+ /Fe 2+ redox potential obtained in any material environment ( Figure 5) [18]. The abnormally high voltage can be explained by the thermodynamic definition of voltage explained in Section 2.2; the edge-sharing geometry of the Fe octahedra in Na 2 Fe 2 (SO 4 ) 3 will raise G charged due to the strong Fe 3+ -Fe 3+ repulsion, leading to high E. Additionally, it offers excellent rate kinetics and cycling stability without requiring any additional cathode optimization. It forms an open framework host for the efficient (de)intercalation of Na ions with very low activation energy. An remarkable feature is that, now, the most commonly accessible redox Fe 3+ /Fe 2+ can, in principle, generate the high voltage of 3.8 V vs. sodium (and hence 4.1 V vs. lithium). However, the hygroscopicity of the sulphate compounds must be carefully managed.

Summary and Perspective
Initiated by Delmas, Goodenough, and co-workers in the 1980s, polyanion-type positive electrode materials now represent a large group of materials for reversible Li + , Na + , and K + insertion. With a suitable combination of transition metal and framework structure, the operating voltage can be tuned, leading sometimes to a suitable high-voltage range for practical application. Although LiFePO4 is the only compound that has been widely applied for commercial use to date, continuous exploration is ongoing in the community toward better batteries with lower cost, high voltage, high safety, and a long calendar life. In addition to the widely examined redox couple based on Fe 3+ /Fe 2+ , Cr 4+ /Cr 3+ could be an inexpensive yet higher-voltage option for future material development in polyanion compounds.  An remarkable feature is that, now, the most commonly accessible redox Fe 3+ /Fe 2+ can, in principle, generate the high voltage of 3.8 V vs. sodium (and hence 4.1 V vs. lithium). However, the hygroscopicity of the sulphate compounds must be carefully managed.

Summary and Perspective
Initiated by Delmas, Goodenough, and co-workers in the 1980s, polyanion-type positive electrode materials now represent a large group of materials for reversible Li + , Na + , and K + insertion. With a suitable combination of transition metal and framework structure, the operating voltage can be tuned, leading sometimes to a suitable high-voltage range for practical application. Although LiFePO 4 is the only compound that has been widely applied for commercial use to date, continuous exploration is ongoing in the community toward better batteries with lower cost, high voltage, high safety, and a long calendar life. In addition to the widely examined redox couple based on Fe 3+ /Fe 2+ , Cr 4+ /Cr 3+ could be an inexpensive yet higher-voltage option for future material development in polyanion compounds.